Question

A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:

(a) the net accelerating force and

(b) the acceleration of the train.

Answer 1

(a) 35000 N (b) 1.944 m/s²

(a)Force exerted by the engine, F = 40000 N

Frictional force offered by the track, F_f = 5000 N

Net accelerating force, F_a = F − F_f = 40000 − 5000 = 35000 N

Hence, the net accelerating force is 35000 N.

(b)Acceleration of the train = a

The engine exerts a force of 40000 N on all the five wagons.

Net accelerating force on the wagons, F_a = 35000 N

Mass of the wagons, m = Mass of a wagon × Number of wagons

Mass of a wagon = 2000 kg

Number of wagons = 5

∴ m = 2000 × 5 = 10000 kg

Total mass of the train, M = m + mass of engine = 10000 + 8000 = 18000 kg

From Newton’s second law of motion:

F_a = Ma

$$\begin{gathered} a=\frac{F_{\mathrm{a}}}{m} \\ =\frac{35000}{18000} \\ =1.944\mathrm{m}{\mathrm{s}}^{-2} \end{gathered}$$

Hence, the acceleration of the train is 1.944 m/s².

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